Map[someFunction,someList] will do someFunction to each member of someList and return a list off all those results. # and & is a cryptic sometimes confusing notation often used for this. The # is the point being operated on and the & indicates to Mathematica that all this is a function.

That tiny little almost invisible "." between rotationMatrix and # is multiplying your matrix times your point.

Try this first on some REALLY simple hand crafted data and rotation matrix. Verify it works on a few points. Try slightly a more complicated rotation matrix and verify that it still works. Verify that a translation vector of {0,0,0} doesn't translate at all. etc, etc, etc.